<?php
    /** PHPExcel root directory */
    if (!defined('PHPEXCEL_ROOT')) {
        /**
         * @ignore
         */
        define('PHPEXCEL_ROOT', dirname(__FILE__) . '/../../');
        require(PHPEXCEL_ROOT . 'PHPExcel/Autoloader.php');
    }
    /** EULER */
    define('EULER', 2.71828182845904523536);

    /**
     * PHPExcel_Calculation_Engineering
     * Copyright (c) 2006 - 2015 PHPExcel
     * This library is free software; you can redistribute it and/or
     * modify it under the terms of the GNU Lesser General Public
     * License as published by the Free Software Foundation; either
     * version 2.1 of the License, or (at your option) any later version.
     * This library is distributed in the hope that it will be useful,
     * but WITHOUT ANY WARRANTY; without even the implied warranty of
     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
     * Lesser General Public License for more details.
     * You should have received a copy of the GNU Lesser General Public
     * License along with this library; if not, write to the Free Software
     * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
     * @category       PHPExcel
     * @package        PHPExcel_Calculation
     * @copyright      Copyright (c) 2006 - 2015 PHPExcel (http://www.codeplex.com/PHPExcel)
     * @license        http://www.gnu.org/licenses/old-licenses/lgpl-2.1.txt    LGPL
     * @version        ##VERSION##, ##DATE##
     */
    class PHPExcel_Calculation_Engineering {
        /**
         * Details of the Units of measure that can be used in CONVERTUOM()
         * @var mixed[]
         */
        private static $conversionUnits = [
            'g'     => [
                'Group'       => 'Mass',
                'Unit Name'   => 'Gram',
                'AllowPrefix' => true
            ],
            'sg'    => [
                'Group'       => 'Mass',
                'Unit Name'   => 'Slug',
                'AllowPrefix' => false
            ],
            'lbm'   => [
                'Group'       => 'Mass',
                'Unit Name'   => 'Pound mass (avoirdupois)',
                'AllowPrefix' => false
            ],
            'u'     => [
                'Group'       => 'Mass',
                'Unit Name'   => 'U (atomic mass unit)',
                'AllowPrefix' => true
            ],
            'ozm'   => [
                'Group'       => 'Mass',
                'Unit Name'   => 'Ounce mass (avoirdupois)',
                'AllowPrefix' => false
            ],
            'm'     => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Meter',
                'AllowPrefix' => true
            ],
            'mi'    => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Statute mile',
                'AllowPrefix' => false
            ],
            'Nmi'   => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Nautical mile',
                'AllowPrefix' => false
            ],
            'in'    => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Inch',
                'AllowPrefix' => false
            ],
            'ft'    => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Foot',
                'AllowPrefix' => false
            ],
            'yd'    => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Yard',
                'AllowPrefix' => false
            ],
            'ang'   => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Angstrom',
                'AllowPrefix' => true
            ],
            'Pica'  => [
                'Group'       => 'Distance',
                'Unit Name'   => 'Pica (1/72 in)',
                'AllowPrefix' => false
            ],
            'yr'    => [
                'Group'       => 'Time',
                'Unit Name'   => 'Year',
                'AllowPrefix' => false
            ],
            'day'   => [
                'Group'       => 'Time',
                'Unit Name'   => 'Day',
                'AllowPrefix' => false
            ],
            'hr'    => [
                'Group'       => 'Time',
                'Unit Name'   => 'Hour',
                'AllowPrefix' => false
            ],
            'mn'    => [
                'Group'       => 'Time',
                'Unit Name'   => 'Minute',
                'AllowPrefix' => false
            ],
            'sec'   => [
                'Group'       => 'Time',
                'Unit Name'   => 'Second',
                'AllowPrefix' => true
            ],
            'Pa'    => [
                'Group'       => 'Pressure',
                'Unit Name'   => 'Pascal',
                'AllowPrefix' => true
            ],
            'p'     => [
                'Group'       => 'Pressure',
                'Unit Name'   => 'Pascal',
                'AllowPrefix' => true
            ],
            'atm'   => [
                'Group'       => 'Pressure',
                'Unit Name'   => 'Atmosphere',
                'AllowPrefix' => true
            ],
            'at'    => [
                'Group'       => 'Pressure',
                'Unit Name'   => 'Atmosphere',
                'AllowPrefix' => true
            ],
            'mmHg'  => [
                'Group'       => 'Pressure',
                'Unit Name'   => 'mm of Mercury',
                'AllowPrefix' => true
            ],
            'N'     => [
                'Group'       => 'Force',
                'Unit Name'   => 'Newton',
                'AllowPrefix' => true
            ],
            'dyn'   => [
                'Group'       => 'Force',
                'Unit Name'   => 'Dyne',
                'AllowPrefix' => true
            ],
            'dy'    => [
                'Group'       => 'Force',
                'Unit Name'   => 'Dyne',
                'AllowPrefix' => true
            ],
            'lbf'   => [
                'Group'       => 'Force',
                'Unit Name'   => 'Pound force',
                'AllowPrefix' => false
            ],
            'J'     => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Joule',
                'AllowPrefix' => true
            ],
            'e'     => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Erg',
                'AllowPrefix' => true
            ],
            'c'     => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Thermodynamic calorie',
                'AllowPrefix' => true
            ],
            'cal'   => [
                'Group'       => 'Energy',
                'Unit Name'   => 'IT calorie',
                'AllowPrefix' => true
            ],
            'eV'    => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Electron volt',
                'AllowPrefix' => true
            ],
            'ev'    => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Electron volt',
                'AllowPrefix' => true
            ],
            'HPh'   => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Horsepower-hour',
                'AllowPrefix' => false
            ],
            'hh'    => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Horsepower-hour',
                'AllowPrefix' => false
            ],
            'Wh'    => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Watt-hour',
                'AllowPrefix' => true
            ],
            'wh'    => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Watt-hour',
                'AllowPrefix' => true
            ],
            'flb'   => [
                'Group'       => 'Energy',
                'Unit Name'   => 'Foot-pound',
                'AllowPrefix' => false
            ],
            'BTU'   => [
                'Group'       => 'Energy',
                'Unit Name'   => 'BTU',
                'AllowPrefix' => false
            ],
            'btu'   => [
                'Group'       => 'Energy',
                'Unit Name'   => 'BTU',
                'AllowPrefix' => false
            ],
            'HP'    => [
                'Group'       => 'Power',
                'Unit Name'   => 'Horsepower',
                'AllowPrefix' => false
            ],
            'h'     => [
                'Group'       => 'Power',
                'Unit Name'   => 'Horsepower',
                'AllowPrefix' => false
            ],
            'W'     => [
                'Group'       => 'Power',
                'Unit Name'   => 'Watt',
                'AllowPrefix' => true
            ],
            'w'     => [
                'Group'       => 'Power',
                'Unit Name'   => 'Watt',
                'AllowPrefix' => true
            ],
            'T'     => [
                'Group'       => 'Magnetism',
                'Unit Name'   => 'Tesla',
                'AllowPrefix' => true
            ],
            'ga'    => [
                'Group'       => 'Magnetism',
                'Unit Name'   => 'Gauss',
                'AllowPrefix' => true
            ],
            'C'     => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Celsius',
                'AllowPrefix' => false
            ],
            'cel'   => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Celsius',
                'AllowPrefix' => false
            ],
            'F'     => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Fahrenheit',
                'AllowPrefix' => false
            ],
            'fah'   => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Fahrenheit',
                'AllowPrefix' => false
            ],
            'K'     => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Kelvin',
                'AllowPrefix' => false
            ],
            'kel'   => [
                'Group'       => 'Temperature',
                'Unit Name'   => 'Kelvin',
                'AllowPrefix' => false
            ],
            'tsp'   => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Teaspoon',
                'AllowPrefix' => false
            ],
            'tbs'   => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Tablespoon',
                'AllowPrefix' => false
            ],
            'oz'    => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Fluid Ounce',
                'AllowPrefix' => false
            ],
            'cup'   => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Cup',
                'AllowPrefix' => false
            ],
            'pt'    => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'U.S. Pint',
                'AllowPrefix' => false
            ],
            'us_pt' => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'U.S. Pint',
                'AllowPrefix' => false
            ],
            'uk_pt' => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'U.K. Pint',
                'AllowPrefix' => false
            ],
            'qt'    => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Quart',
                'AllowPrefix' => false
            ],
            'gal'   => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Gallon',
                'AllowPrefix' => false
            ],
            'l'     => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Litre',
                'AllowPrefix' => true
            ],
            'lt'    => [
                'Group'       => 'Liquid',
                'Unit Name'   => 'Litre',
                'AllowPrefix' => true
            ],
        ];
        /**
         * Details of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
         * @var mixed[]
         */
        private static $conversionMultipliers = [
            'Y' => [
                'multiplier' => 1E24,
                'name'       => 'yotta'
            ],
            'Z' => [
                'multiplier' => 1E21,
                'name'       => 'zetta'
            ],
            'E' => [
                'multiplier' => 1E18,
                'name'       => 'exa'
            ],
            'P' => [
                'multiplier' => 1E15,
                'name'       => 'peta'
            ],
            'T' => [
                'multiplier' => 1E12,
                'name'       => 'tera'
            ],
            'G' => [
                'multiplier' => 1E9,
                'name'       => 'giga'
            ],
            'M' => [
                'multiplier' => 1E6,
                'name'       => 'mega'
            ],
            'k' => [
                'multiplier' => 1E3,
                'name'       => 'kilo'
            ],
            'h' => [
                'multiplier' => 1E2,
                'name'       => 'hecto'
            ],
            'e' => [
                'multiplier' => 1E1,
                'name'       => 'deka'
            ],
            'd' => [
                'multiplier' => 1E-1,
                'name'       => 'deci'
            ],
            'c' => [
                'multiplier' => 1E-2,
                'name'       => 'centi'
            ],
            'm' => [
                'multiplier' => 1E-3,
                'name'       => 'milli'
            ],
            'u' => [
                'multiplier' => 1E-6,
                'name'       => 'micro'
            ],
            'n' => [
                'multiplier' => 1E-9,
                'name'       => 'nano'
            ],
            'p' => [
                'multiplier' => 1E-12,
                'name'       => 'pico'
            ],
            'f' => [
                'multiplier' => 1E-15,
                'name'       => 'femto'
            ],
            'a' => [
                'multiplier' => 1E-18,
                'name'       => 'atto'
            ],
            'z' => [
                'multiplier' => 1E-21,
                'name'       => 'zepto'
            ],
            'y' => [
                'multiplier' => 1E-24,
                'name'       => 'yocto'
            ],
        ];
        /**
         * Details of the Units of measure conversion factors, organised by group
         * @var mixed[]
         */
        private static $unitConversions = [
            'Mass'      => [
                'g'   => [
                    'g'   => 1.0,
                    'sg'  => 6.85220500053478E-05,
                    'lbm' => 2.20462291469134E-03,
                    'u'   => 6.02217000000000E+23,
                    'ozm' => 3.52739718003627E-02,
                ],
                'sg'  => [
                    'g'   => 1.45938424189287E+04,
                    'sg'  => 1.0,
                    'lbm' => 3.21739194101647E+01,
                    'u'   => 8.78866000000000E+27,
                    'ozm' => 5.14782785944229E+02,
                ],
                'lbm' => [
                    'g'   => 4.5359230974881148E+02,
                    'sg'  => 3.10810749306493E-02,
                    'lbm' => 1.0,
                    'u'   => 2.73161000000000E+26,
                    'ozm' => 1.60000023429410E+01,
                ],
                'u'   => [
                    'g'   => 1.66053100460465E-24,
                    'sg'  => 1.13782988532950E-28,
                    'lbm' => 3.66084470330684E-27,
                    'u'   => 1.0,
                    'ozm' => 5.85735238300524E-26,
                ],
                'ozm' => [
                    'g'   => 2.83495152079732E+01,
                    'sg'  => 1.94256689870811E-03,
                    'lbm' => 6.24999908478882E-02,
                    'u'   => 1.70725600000000E+25,
                    'ozm' => 1.0,
                ],
            ],
            'Distance'  => [
                'm'    => [
                    'm'    => 1.0,
                    'mi'   => 6.21371192237334E-04,
                    'Nmi'  => 5.39956803455724E-04,
                    'in'   => 3.93700787401575E+01,
                    'ft'   => 3.28083989501312E+00,
                    'yd'   => 1.09361329797891E+00,
                    'ang'  => 1.00000000000000E+10,
                    'Pica' => 2.83464566929116E+03,
                ],
                'mi'   => [
                    'm'    => 1.60934400000000E+03,
                    'mi'   => 1.0,
                    'Nmi'  => 8.68976241900648E-01,
                    'in'   => 6.33600000000000E+04,
                    'ft'   => 5.28000000000000E+03,
                    'yd'   => 1.76000000000000E+03,
                    'ang'  => 1.60934400000000E+13,
                    'Pica' => 4.56191999999971E+06,
                ],
                'Nmi'  => [
                    'm'    => 1.85200000000000E+03,
                    'mi'   => 1.15077944802354E+00,
                    'Nmi'  => 1.0,
                    'in'   => 7.29133858267717E+04,
                    'ft'   => 6.07611548556430E+03,
                    'yd'   => 2.02537182785694E+03,
                    'ang'  => 1.85200000000000E+13,
                    'Pica' => 5.24976377952723E+06,
                ],
                'in'   => [
                    'm'    => 2.54000000000000E-02,
                    'mi'   => 1.57828282828283E-05,
                    'Nmi'  => 1.37149028077754E-05,
                    'in'   => 1.0,
                    'ft'   => 8.33333333333333E-02,
                    'yd'   => 2.77777777686643E-02,
                    'ang'  => 2.54000000000000E+08,
                    'Pica' => 7.19999999999955E+01,
                ],
                'ft'   => [
                    'm'    => 3.04800000000000E-01,
                    'mi'   => 1.89393939393939E-04,
                    'Nmi'  => 1.64578833693305E-04,
                    'in'   => 1.20000000000000E+01,
                    'ft'   => 1.0,
                    'yd'   => 3.33333333223972E-01,
                    'ang'  => 3.04800000000000E+09,
                    'Pica' => 8.63999999999946E+02,
                ],
                'yd'   => [
                    'm'    => 9.14400000300000E-01,
                    'mi'   => 5.68181818368230E-04,
                    'Nmi'  => 4.93736501241901E-04,
                    'in'   => 3.60000000118110E+01,
                    'ft'   => 3.00000000000000E+00,
                    'yd'   => 1.0,
                    'ang'  => 9.14400000300000E+09,
                    'Pica' => 2.59200000085023E+03,
                ],
                'ang'  => [
                    'm'    => 1.00000000000000E-10,
                    'mi'   => 6.21371192237334E-14,
                    'Nmi'  => 5.39956803455724E-14,
                    'in'   => 3.93700787401575E-09,
                    'ft'   => 3.28083989501312E-10,
                    'yd'   => 1.09361329797891E-10,
                    'ang'  => 1.0,
                    'Pica' => 2.83464566929116E-07,
                ],
                'Pica' => [
                    'm'    => 3.52777777777800E-04,
                    'mi'   => 2.19205948372629E-07,
                    'Nmi'  => 1.90484761219114E-07,
                    'in'   => 1.38888888888898E-02,
                    'ft'   => 1.15740740740748E-03,
                    'yd'   => 3.85802469009251E-04,
                    'ang'  => 3.52777777777800E+06,
                    'Pica' => 1.0,
                ],
            ],
            'Time'      => [
                'yr'  => [
                    'yr'  => 1.0,
                    'day' => 365.25,
                    'hr'  => 8766.0,
                    'mn'  => 525960.0,
                    'sec' => 31557600.0,
                ],
                'day' => [
                    'yr'  => 2.73785078713210E-03,
                    'day' => 1.0,
                    'hr'  => 24.0,
                    'mn'  => 1440.0,
                    'sec' => 86400.0,
                ],
                'hr'  => [
                    'yr'  => 1.14077116130504E-04,
                    'day' => 4.16666666666667E-02,
                    'hr'  => 1.0,
                    'mn'  => 60.0,
                    'sec' => 3600.0,
                ],
                'mn'  => [
                    'yr'  => 1.90128526884174E-06,
                    'day' => 6.94444444444444E-04,
                    'hr'  => 1.66666666666667E-02,
                    'mn'  => 1.0,
                    'sec' => 60.0,
                ],
                'sec' => [
                    'yr'  => 3.16880878140289E-08,
                    'day' => 1.15740740740741E-05,
                    'hr'  => 2.77777777777778E-04,
                    'mn'  => 1.66666666666667E-02,
                    'sec' => 1.0,
                ],
            ],
            'Pressure'  => [
                'Pa'   => [
                    'Pa'   => 1.0,
                    'p'    => 1.0,
                    'atm'  => 9.86923299998193E-06,
                    'at'   => 9.86923299998193E-06,
                    'mmHg' => 7.50061707998627E-03,
                ],
                'p'    => [
                    'Pa'   => 1.0,
                    'p'    => 1.0,
                    'atm'  => 9.86923299998193E-06,
                    'at'   => 9.86923299998193E-06,
                    'mmHg' => 7.50061707998627E-03,
                ],
                'atm'  => [
                    'Pa'   => 1.01324996583000E+05,
                    'p'    => 1.01324996583000E+05,
                    'atm'  => 1.0,
                    'at'   => 1.0,
                    'mmHg' => 760.0,
                ],
                'at'   => [
                    'Pa'   => 1.01324996583000E+05,
                    'p'    => 1.01324996583000E+05,
                    'atm'  => 1.0,
                    'at'   => 1.0,
                    'mmHg' => 760.0,
                ],
                'mmHg' => [
                    'Pa'   => 1.33322363925000E+02,
                    'p'    => 1.33322363925000E+02,
                    'atm'  => 1.31578947368421E-03,
                    'at'   => 1.31578947368421E-03,
                    'mmHg' => 1.0,
                ],
            ],
            'Force'     => [
                'N'   => [
                    'N'   => 1.0,
                    'dyn' => 1.0E+5,
                    'dy'  => 1.0E+5,
                    'lbf' => 2.24808923655339E-01,
                ],
                'dyn' => [
                    'N'   => 1.0E-5,
                    'dyn' => 1.0,
                    'dy'  => 1.0,
                    'lbf' => 2.24808923655339E-06,
                ],
                'dy'  => [
                    'N'   => 1.0E-5,
                    'dyn' => 1.0,
                    'dy'  => 1.0,
                    'lbf' => 2.24808923655339E-06,
                ],
                'lbf' => [
                    'N'   => 4.448222,
                    'dyn' => 4.448222E+5,
                    'dy'  => 4.448222E+5,
                    'lbf' => 1.0,
                ],
            ],
            'Energy'    => [
                'J'   => [
                    'J'   => 1.0,
                    'e'   => 9.99999519343231E+06,
                    'c'   => 2.39006249473467E-01,
                    'cal' => 2.38846190642017E-01,
                    'eV'  => 6.24145700000000E+18,
                    'ev'  => 6.24145700000000E+18,
                    'HPh' => 3.72506430801000E-07,
                    'hh'  => 3.72506430801000E-07,
                    'Wh'  => 2.77777916238711E-04,
                    'wh'  => 2.77777916238711E-04,
                    'flb' => 2.37304222192651E+01,
                    'BTU' => 9.47815067349015E-04,
                    'btu' => 9.47815067349015E-04,
                ],
                'e'   => [
                    'J'   => 1.00000048065700E-07,
                    'e'   => 1.0,
                    'c'   => 2.39006364353494E-08,
                    'cal' => 2.38846305445111E-08,
                    'eV'  => 6.24146000000000E+11,
                    'ev'  => 6.24146000000000E+11,
                    'HPh' => 3.72506609848824E-14,
                    'hh'  => 3.72506609848824E-14,
                    'Wh'  => 2.77778049754611E-11,
                    'wh'  => 2.77778049754611E-11,
                    'flb' => 2.37304336254586E-06,
                    'BTU' => 9.47815522922962E-11,
                    'btu' => 9.47815522922962E-11,
                ],
                'c'   => [
                    'J'   => 4.18399101363672E+00,
                    'e'   => 4.18398900257312E+07,
                    'c'   => 1.0,
                    'cal' => 9.99330315287563E-01,
                    'eV'  => 2.61142000000000E+19,
                    'ev'  => 2.61142000000000E+19,
                    'HPh' => 1.55856355899327E-06,
                    'hh'  => 1.55856355899327E-06,
                    'Wh'  => 1.16222030532950E-03,
                    'wh'  => 1.16222030532950E-03,
                    'flb' => 9.92878733152102E+01,
                    'BTU' => 3.96564972437776E-03,
                    'btu' => 3.96564972437776E-03,
                ],
                'cal' => [
                    'J'   => 4.18679484613929E+00,
                    'e'   => 4.18679283372801E+07,
                    'c'   => 1.00067013349059E+00,
                    'cal' => 1.0,
                    'eV'  => 2.61317000000000E+19,
                    'ev'  => 2.61317000000000E+19,
                    'HPh' => 1.55960800463137E-06,
                    'hh'  => 1.55960800463137E-06,
                    'Wh'  => 1.16299914807955E-03,
                    'wh'  => 1.16299914807955E-03,
                    'flb' => 9.93544094443283E+01,
                    'BTU' => 3.96830723907002E-03,
                    'btu' => 3.96830723907002E-03,
                ],
                'eV'  => [
                    'J'   => 1.60219000146921E-19,
                    'e'   => 1.60218923136574E-12,
                    'c'   => 3.82933423195043E-20,
                    'cal' => 3.82676978535648E-20,
                    'eV'  => 1.0,
                    'ev'  => 1.0,
                    'HPh' => 5.96826078912344E-26,
                    'hh'  => 5.96826078912344E-26,
                    'Wh'  => 4.45053000026614E-23,
                    'wh'  => 4.45053000026614E-23,
                    'flb' => 3.80206452103492E-18,
                    'BTU' => 1.51857982414846E-22,
                    'btu' => 1.51857982414846E-22,
                ],
                'ev'  => [
                    'J'   => 1.60219000146921E-19,
                    'e'   => 1.60218923136574E-12,
                    'c'   => 3.82933423195043E-20,
                    'cal' => 3.82676978535648E-20,
                    'eV'  => 1.0,
                    'ev'  => 1.0,
                    'HPh' => 5.96826078912344E-26,
                    'hh'  => 5.96826078912344E-26,
                    'Wh'  => 4.45053000026614E-23,
                    'wh'  => 4.45053000026614E-23,
                    'flb' => 3.80206452103492E-18,
                    'BTU' => 1.51857982414846E-22,
                    'btu' => 1.51857982414846E-22,
                ],
                'HPh' => [
                    'J'   => 2.68451741316170E+06,
                    'e'   => 2.68451612283024E+13,
                    'c'   => 6.41616438565991E+05,
                    'cal' => 6.41186757845835E+05,
                    'eV'  => 1.67553000000000E+25,
                    'ev'  => 1.67553000000000E+25,
                    'HPh' => 1.0,
                    'hh'  => 1.0,
                    'Wh'  => 7.45699653134593E+02,
                    'wh'  => 7.45699653134593E+02,
                    'flb' => 6.37047316692964E+07,
                    'BTU' => 2.54442605275546E+03,
                    'btu' => 2.54442605275546E+03,
                ],
                'hh'  => [
                    'J'   => 2.68451741316170E+06,
                    'e'   => 2.68451612283024E+13,
                    'c'   => 6.41616438565991E+05,
                    'cal' => 6.41186757845835E+05,
                    'eV'  => 1.67553000000000E+25,
                    'ev'  => 1.67553000000000E+25,
                    'HPh' => 1.0,
                    'hh'  => 1.0,
                    'Wh'  => 7.45699653134593E+02,
                    'wh'  => 7.45699653134593E+02,
                    'flb' => 6.37047316692964E+07,
                    'BTU' => 2.54442605275546E+03,
                    'btu' => 2.54442605275546E+03,
                ],
                'Wh'  => [
                    'J'   => 3.59999820554720E+03,
                    'e'   => 3.59999647518369E+10,
                    'c'   => 8.60422069219046E+02,
                    'cal' => 8.59845857713046E+02,
                    'eV'  => 2.24692340000000E+22,
                    'ev'  => 2.24692340000000E+22,
                    'HPh' => 1.34102248243839E-03,
                    'hh'  => 1.34102248243839E-03,
                    'Wh'  => 1.0,
                    'wh'  => 1.0,
                    'flb' => 8.54294774062316E+04,
                    'BTU' => 3.41213254164705E+00,
                    'btu' => 3.41213254164705E+00,
                ],
                'wh'  => [
                    'J'   => 3.59999820554720E+03,
                    'e'   => 3.59999647518369E+10,
                    'c'   => 8.60422069219046E+02,
                    'cal' => 8.59845857713046E+02,
                    'eV'  => 2.24692340000000E+22,
                    'ev'  => 2.24692340000000E+22,
                    'HPh' => 1.34102248243839E-03,
                    'hh'  => 1.34102248243839E-03,
                    'Wh'  => 1.0,
                    'wh'  => 1.0,
                    'flb' => 8.54294774062316E+04,
                    'BTU' => 3.41213254164705E+00,
                    'btu' => 3.41213254164705E+00,
                ],
                'flb' => [
                    'J'   => 4.21400003236424E-02,
                    'e'   => 4.21399800687660E+05,
                    'c'   => 1.00717234301644E-02,
                    'cal' => 1.00649785509554E-02,
                    'eV'  => 2.63015000000000E+17,
                    'ev'  => 2.63015000000000E+17,
                    'HPh' => 1.56974211145130E-08,
                    'hh'  => 1.56974211145130E-08,
                    'Wh'  => 1.17055614802000E-05,
                    'wh'  => 1.17055614802000E-05,
                    'flb' => 1.0,
                    'BTU' => 3.99409272448406E-05,
                    'btu' => 3.99409272448406E-05,
                ],
                'BTU' => [
                    'J'   => 1.05505813786749E+03,
                    'e'   => 1.05505763074665E+10,
                    'c'   => 2.52165488508168E+02,
                    'cal' => 2.51996617135510E+02,
                    'eV'  => 6.58510000000000E+21,
                    'ev'  => 6.58510000000000E+21,
                    'HPh' => 3.93015941224568E-04,
                    'hh'  => 3.93015941224568E-04,
                    'Wh'  => 2.93071851047526E-01,
                    'wh'  => 2.93071851047526E-01,
                    'flb' => 2.50369750774671E+04,
                    'BTU' => 1.0,
                    'btu' => 1.0,
                ],
                'btu' => [
                    'J'   => 1.05505813786749E+03,
                    'e'   => 1.05505763074665E+10,
                    'c'   => 2.52165488508168E+02,
                    'cal' => 2.51996617135510E+02,
                    'eV'  => 6.58510000000000E+21,
                    'ev'  => 6.58510000000000E+21,
                    'HPh' => 3.93015941224568E-04,
                    'hh'  => 3.93015941224568E-04,
                    'Wh'  => 2.93071851047526E-01,
                    'wh'  => 2.93071851047526E-01,
                    'flb' => 2.50369750774671E+04,
                    'BTU' => 1.0,
                    'btu' => 1.0,
                ],
            ],
            'Power'     => [
                'HP' => [
                    'HP' => 1.0,
                    'h'  => 1.0,
                    'W'  => 7.45701000000000E+02,
                    'w'  => 7.45701000000000E+02,
                ],
                'h'  => [
                    'HP' => 1.0,
                    'h'  => 1.0,
                    'W'  => 7.45701000000000E+02,
                    'w'  => 7.45701000000000E+02,
                ],
                'W'  => [
                    'HP' => 1.34102006031908E-03,
                    'h'  => 1.34102006031908E-03,
                    'W'  => 1.0,
                    'w'  => 1.0,
                ],
                'w'  => [
                    'HP' => 1.34102006031908E-03,
                    'h'  => 1.34102006031908E-03,
                    'W'  => 1.0,
                    'w'  => 1.0,
                ],
            ],
            'Magnetism' => [
                'T'  => [
                    'T'  => 1.0,
                    'ga' => 10000.0,
                ],
                'ga' => [
                    'T'  => 0.0001,
                    'ga' => 1.0,
                ],
            ],
            'Liquid'    => [
                'tsp'   => [
                    'tsp'   => 1.0,
                    'tbs'   => 3.33333333333333E-01,
                    'oz'    => 1.66666666666667E-01,
                    'cup'   => 2.08333333333333E-02,
                    'pt'    => 1.04166666666667E-02,
                    'us_pt' => 1.04166666666667E-02,
                    'uk_pt' => 8.67558516821960E-03,
                    'qt'    => 5.20833333333333E-03,
                    'gal'   => 1.30208333333333E-03,
                    'l'     => 4.92999408400710E-03,
                    'lt'    => 4.92999408400710E-03,
                ],
                'tbs'   => [
                    'tsp'   => 3.00000000000000E+00,
                    'tbs'   => 1.0,
                    'oz'    => 5.00000000000000E-01,
                    'cup'   => 6.25000000000000E-02,
                    'pt'    => 3.12500000000000E-02,
                    'us_pt' => 3.12500000000000E-02,
                    'uk_pt' => 2.60267555046588E-02,
                    'qt'    => 1.56250000000000E-02,
                    'gal'   => 3.90625000000000E-03,
                    'l'     => 1.47899822520213E-02,
                    'lt'    => 1.47899822520213E-02,
                ],
                'oz'    => [
                    'tsp'   => 6.00000000000000E+00,
                    'tbs'   => 2.00000000000000E+00,
                    'oz'    => 1.0,
                    'cup'   => 1.25000000000000E-01,
                    'pt'    => 6.25000000000000E-02,
                    'us_pt' => 6.25000000000000E-02,
                    'uk_pt' => 5.20535110093176E-02,
                    'qt'    => 3.12500000000000E-02,
                    'gal'   => 7.81250000000000E-03,
                    'l'     => 2.95799645040426E-02,
                    'lt'    => 2.95799645040426E-02,
                ],
                'cup'   => [
                    'tsp'   => 4.80000000000000E+01,
                    'tbs'   => 1.60000000000000E+01,
                    'oz'    => 8.00000000000000E+00,
                    'cup'   => 1.0,
                    'pt'    => 5.00000000000000E-01,
                    'us_pt' => 5.00000000000000E-01,
                    'uk_pt' => 4.16428088074541E-01,
                    'qt'    => 2.50000000000000E-01,
                    'gal'   => 6.25000000000000E-02,
                    'l'     => 2.36639716032341E-01,
                    'lt'    => 2.36639716032341E-01,
                ],
                'pt'    => [
                    'tsp'   => 9.60000000000000E+01,
                    'tbs'   => 3.20000000000000E+01,
                    'oz'    => 1.60000000000000E+01,
                    'cup'   => 2.00000000000000E+00,
                    'pt'    => 1.0,
                    'us_pt' => 1.0,
                    'uk_pt' => 8.32856176149081E-01,
                    'qt'    => 5.00000000000000E-01,
                    'gal'   => 1.25000000000000E-01,
                    'l'     => 4.73279432064682E-01,
                    'lt'    => 4.73279432064682E-01,
                ],
                'us_pt' => [
                    'tsp'   => 9.60000000000000E+01,
                    'tbs'   => 3.20000000000000E+01,
                    'oz'    => 1.60000000000000E+01,
                    'cup'   => 2.00000000000000E+00,
                    'pt'    => 1.0,
                    'us_pt' => 1.0,
                    'uk_pt' => 8.32856176149081E-01,
                    'qt'    => 5.00000000000000E-01,
                    'gal'   => 1.25000000000000E-01,
                    'l'     => 4.73279432064682E-01,
                    'lt'    => 4.73279432064682E-01,
                ],
                'uk_pt' => [
                    'tsp'   => 1.15266000000000E+02,
                    'tbs'   => 3.84220000000000E+01,
                    'oz'    => 1.92110000000000E+01,
                    'cup'   => 2.40137500000000E+00,
                    'pt'    => 1.20068750000000E+00,
                    'us_pt' => 1.20068750000000E+00,
                    'uk_pt' => 1.0,
                    'qt'    => 6.00343750000000E-01,
                    'gal'   => 1.50085937500000E-01,
                    'l'     => 5.68260698087162E-01,
                    'lt'    => 5.68260698087162E-01,
                ],
                'qt'    => [
                    'tsp'   => 1.92000000000000E+02,
                    'tbs'   => 6.40000000000000E+01,
                    'oz'    => 3.20000000000000E+01,
                    'cup'   => 4.00000000000000E+00,
                    'pt'    => 2.00000000000000E+00,
                    'us_pt' => 2.00000000000000E+00,
                    'uk_pt' => 1.66571235229816E+00,
                    'qt'    => 1.0,
                    'gal'   => 2.50000000000000E-01,
                    'l'     => 9.46558864129363E-01,
                    'lt'    => 9.46558864129363E-01,
                ],
                'gal'   => [
                    'tsp'   => 7.68000000000000E+02,
                    'tbs'   => 2.56000000000000E+02,
                    'oz'    => 1.28000000000000E+02,
                    'cup'   => 1.60000000000000E+01,
                    'pt'    => 8.00000000000000E+00,
                    'us_pt' => 8.00000000000000E+00,
                    'uk_pt' => 6.66284940919265E+00,
                    'qt'    => 4.00000000000000E+00,
                    'gal'   => 1.0,
                    'l'     => 3.78623545651745E+00,
                    'lt'    => 3.78623545651745E+00,
                ],
                'l'     => [
                    'tsp'   => 2.02840000000000E+02,
                    'tbs'   => 6.76133333333333E+01,
                    'oz'    => 3.38066666666667E+01,
                    'cup'   => 4.22583333333333E+00,
                    'pt'    => 2.11291666666667E+00,
                    'us_pt' => 2.11291666666667E+00,
                    'uk_pt' => 1.75975569552166E+00,
                    'qt'    => 1.05645833333333E+00,
                    'gal'   => 2.64114583333333E-01,
                    'l'     => 1.0,
                    'lt'    => 1.0,
                ],
                'lt'    => [
                    'tsp'   => 2.02840000000000E+02,
                    'tbs'   => 6.76133333333333E+01,
                    'oz'    => 3.38066666666667E+01,
                    'cup'   => 4.22583333333333E+00,
                    'pt'    => 2.11291666666667E+00,
                    'us_pt' => 2.11291666666667E+00,
                    'uk_pt' => 1.75975569552166E+00,
                    'qt'    => 1.05645833333333E+00,
                    'gal'   => 2.64114583333333E-01,
                    'l'     => 1.0,
                    'lt'    => 1.0,
                ],
            ],
        ];
        private static $twoSqrtPi       = 1.128379167095512574;
        private static $oneSqrtPi       = 0.564189583547756287;

        /**
         *    BESSELK
         *    Returns the modified Bessel function Kn(x), which is equivalent to the Bessel functions evaluated
         *        for purely imaginary arguments.
         *    Excel Function:
         *        BESSELK(x,ord)
         * @access    public
         * @category  Engineering Functions
         * @param    float   $x           The value at which to evaluate the function.
         *                                If x is nonnumeric, BESSELK returns the #VALUE! error value.
         * @param    integer $ord         The order of the Bessel function. If n is not an integer, it is truncated.
         *                                If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
         *                                If $ord < 0, BESSELK returns the #NUM! error value.
         * @return    float
         */
        public static function BESSELK($x, $ord) {
            $x   = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
            if ((is_numeric($x)) && (is_numeric($ord))) {
                if (($ord < 0) || ($x == 0.0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                switch (floor($ord)) {
                    case 0:
                        return self::besselK0($x);
                    case 1:
                        return self::besselK1($x);
                    default:
                        $fTox = 2 / $x;
                        $fBkm = self::besselK0($x);
                        $fBk  = self::besselK1($x);
                        for ($n = 1; $n < $ord; ++$n) {
                            $fBkp = $fBkm + $n * $fTox * $fBk;
                            $fBkm = $fBk;
                            $fBk  = $fBkp;
                        }
                }
                return (is_nan($fBk)) ? PHPExcel_Calculation_Functions::NaN() : $fBk;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        private static function besselK0($fNum) {
            if ($fNum <= 2) {
                $fNum2 = $fNum * 0.5;
                $y     = ($fNum2 * $fNum2);
                $fRet  = -log($fNum2) * self::BESSELI($fNum, 0) + (-0.57721566 + $y * (0.42278420 + $y * (0.23069756 + $y * (0.3488590e-1 + $y * (0.262698e-2 + $y * (0.10750e-3 + $y * 0.74e-5))))));
            } else {
                $y    = 2 / $fNum;
                $fRet = exp(-$fNum) / sqrt($fNum) * (1.25331414 + $y * (-0.7832358e-1 + $y * (0.2189568e-1 + $y * (-0.1062446e-1 + $y * (0.587872e-2 + $y * (-0.251540e-2 + $y * 0.53208e-3))))));
            }
            return $fRet;
        }

        /**
         *    BESSELI
         *    Returns the modified Bessel function In(x), which is equivalent to the Bessel function evaluated
         *        for purely imaginary arguments
         *    Excel Function:
         *        BESSELI(x,ord)
         * @access    public
         * @category  Engineering Functions
         * @param    float   $x           The value at which to evaluate the function.
         *                                If x is nonnumeric, BESSELI returns the #VALUE! error value.
         * @param    integer $ord         The order of the Bessel function.
         *                                If ord is not an integer, it is truncated.
         *                                If $ord is nonnumeric, BESSELI returns the #VALUE! error value.
         *                                If $ord < 0, BESSELI returns the #NUM! error value.
         * @return    float
         */
        public static function BESSELI($x, $ord) {
            $x   = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
            if ((is_numeric($x)) && (is_numeric($ord))) {
                $ord = floor($ord);
                if ($ord < 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                if (abs($x) <= 30) {
                    $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
                    $ordK    = 1;
                    $fSqrX   = ($x * $x) / 4;
                    do {
                        $fTerm   *= $fSqrX;
                        $fTerm   /= ($ordK * ($ordK + $ord));
                        $fResult += $fTerm;
                    } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
                } else {
                    $f_2_PI = 2 * M_PI;
                    $fXAbs   = abs($x);
                    $fResult = exp($fXAbs) / sqrt($f_2_PI * $fXAbs);
                    if (($ord & 1) && ($x < 0)) {
                        $fResult = -$fResult;
                    }
                }
                return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        private static function besselK1($fNum) {
            if ($fNum <= 2) {
                $fNum2 = $fNum * 0.5;
                $y     = ($fNum2 * $fNum2);
                $fRet  = log($fNum2) * self::BESSELI($fNum, 1) + (1 + $y * (0.15443144 + $y * (-0.67278579 + $y * (-0.18156897 + $y * (-0.1919402e-1 + $y * (-0.110404e-2 + $y * (-0.4686e-4))))))) / $fNum;
            } else {
                $y    = 2 / $fNum;
                $fRet = exp(-$fNum) / sqrt($fNum) * (1.25331414 + $y * (0.23498619 + $y * (-0.3655620e-1 + $y * (0.1504268e-1 + $y * (-0.780353e-2 + $y * (0.325614e-2 + $y * (-0.68245e-3)))))));
            }
            return $fRet;
        }

        /**
         *    BESSELY
         *    Returns the Bessel function, which is also called the Weber function or the Neumann function.
         *    Excel Function:
         *        BESSELY(x,ord)
         * @access    public
         * @category  Engineering Functions
         * @param    float   $x           The value at which to evaluate the function.
         *                                If x is nonnumeric, BESSELK returns the #VALUE! error value.
         * @param    integer $ord         The order of the Bessel function. If n is not an integer, it is truncated.
         *                                If $ord is nonnumeric, BESSELK returns the #VALUE! error value.
         *                                If $ord < 0, BESSELK returns the #NUM! error value.
         * @return    float
         */
        public static function BESSELY($x, $ord) {
            $x   = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
            if ((is_numeric($x)) && (is_numeric($ord))) {
                if (($ord < 0) || ($x == 0.0)) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                switch (floor($ord)) {
                    case 0:
                        return self::besselY0($x);
                    case 1:
                        return self::besselY1($x);
                    default:
                        $fTox = 2 / $x;
                        $fBym = self::besselY0($x);
                        $fBy  = self::besselY1($x);
                        for ($n = 1; $n < $ord; ++$n) {
                            $fByp = $n * $fTox * $fBy - $fBym;
                            $fBym = $fBy;
                            $fBy  = $fByp;
                        }
                }
                return (is_nan($fBy)) ? PHPExcel_Calculation_Functions::NaN() : $fBy;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        private static function besselY0($fNum) {
            if ($fNum < 8.0) {
                $y    = ($fNum * $fNum);
                $f1   = -2957821389.0 + $y * (7062834065.0 + $y * (-512359803.6 + $y * (10879881.29 + $y * (-86327.92757 + $y * 228.4622733))));
                $f2   = 40076544269.0 + $y * (745249964.8 + $y * (7189466.438 + $y * (47447.26470 + $y * (226.1030244 + $y))));
                $fRet = $f1 / $f2 + 0.636619772 * self::BESSELJ($fNum, 0) * log($fNum);
            } else {
                $z    = 8.0 / $fNum;
                $y    = ($z * $z);
                $xx   = $fNum - 0.785398164;
                $f1   = 1 + $y * (-0.1098628627e-2 + $y * (0.2734510407e-4 + $y * (-0.2073370639e-5 + $y * 0.2093887211e-6)));
                $f2   = -0.1562499995e-1 + $y * (0.1430488765e-3 + $y * (-0.6911147651e-5 + $y * (0.7621095161e-6 + $y * (-0.934945152e-7))));
                $fRet = sqrt(0.636619772 / $fNum) * (sin($xx) * $f1 + $z * cos($xx) * $f2);
            }
            return $fRet;
        }

        /**
         *    BESSELJ
         *    Returns the Bessel function
         *    Excel Function:
         *        BESSELJ(x,ord)
         * @access    public
         * @category  Engineering Functions
         * @param    float   $x           The value at which to evaluate the function.
         *                                If x is nonnumeric, BESSELJ returns the #VALUE! error value.
         * @param    integer $ord         The order of the Bessel function. If n is not an integer, it is truncated.
         *                                If $ord is nonnumeric, BESSELJ returns the #VALUE! error value.
         *                                If $ord < 0, BESSELJ returns the #NUM! error value.
         * @return    float
         */
        public static function BESSELJ($x, $ord) {
            $x   = (is_null($x)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $ord = (is_null($ord)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($ord);
            if ((is_numeric($x)) && (is_numeric($ord))) {
                $ord = floor($ord);
                if ($ord < 0) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $fResult = 0;
                if (abs($x) <= 30) {
                    $fResult = $fTerm = pow($x / 2, $ord) / PHPExcel_Calculation_MathTrig::FACT($ord);
                    $ordK    = 1;
                    $fSqrX   = ($x * $x) / -4;
                    do {
                        $fTerm   *= $fSqrX;
                        $fTerm   /= ($ordK * ($ordK + $ord));
                        $fResult += $fTerm;
                    } while ((abs($fTerm) > 1e-12) && (++$ordK < 100));
                } else {
                    $f_PI_DIV_2 = M_PI / 2;
                    $f_PI_DIV_4 = M_PI / 4;
                    $fXAbs   = abs($x);
                    $fResult = sqrt(M_2DIVPI / $fXAbs) * cos($fXAbs - $ord * $f_PI_DIV_2 - $f_PI_DIV_4);
                    if (($ord & 1) && ($x < 0)) {
                        $fResult = -$fResult;
                    }
                }
                return (is_nan($fResult)) ? PHPExcel_Calculation_Functions::NaN() : $fResult;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        private static function besselY1($fNum) {
            if ($fNum < 8.0) {
                $y    = ($fNum * $fNum);
                $f1   = $fNum * (-0.4900604943e13 + $y * (0.1275274390e13 + $y * (-0.5153438139e11 + $y * (0.7349264551e9 + $y * (-0.4237922726e7 + $y * 0.8511937935e4)))));
                $f2   = 0.2499580570e14 + $y * (0.4244419664e12 + $y * (0.3733650367e10 + $y * (0.2245904002e8 + $y * (0.1020426050e6 + $y * (0.3549632885e3 + $y)))));
                $fRet = $f1 / $f2 + 0.636619772 * (self::BESSELJ($fNum, 1) * log($fNum) - 1 / $fNum);
            } else {
                $fRet = sqrt(0.636619772 / $fNum) * sin($fNum - 2.356194491);
            }
            return $fRet;
        }

        /**
         * BINTODEC
         * Return a binary value as decimal.
         * Excel Function:
         *        BIN2DEC(x)
         * @access    public
         * @category  Engineering Functions
         * @param    string $x            The binary number (as a string) that you want to convert. The number
         *                                cannot contain more than 10 characters (10 bits). The most significant
         *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                Negative numbers are represented using two's-complement notation.
         *                                If number is not a valid binary number, or if number contains more than
         *                                10 characters (10 bits), BIN2DEC returns the #NUM! error value.
         * @return    string
         */
        public static function BINTODEC($x) {
            $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                $x = floor($x);
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if (strlen($x) > 10) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (strlen($x) == 10) {
                //    Two's Complement
                $x = substr($x, -9);
                return '-' . (512 - bindec($x));
            }
            return bindec($x);
        }

        /**
         * BINTOHEX
         * Return a binary value as hex.
         * Excel Function:
         *        BIN2HEX(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x           The binary number (as a string) that you want to convert. The number
         *                                cannot contain more than 10 characters (10 bits). The most significant
         *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                Negative numbers are represented using two's-complement notation.
         *                                If number is not a valid binary number, or if number contains more than
         *                                10 characters (10 bits), BIN2HEX returns the #NUM! error value.
         * @param    integer $places      The number of characters to use. If places is omitted, BIN2HEX uses the
         *                                minimum number of characters necessary. Places is useful for padding the
         *                                return value with leading 0s (zeros).
         *                                If places is not an integer, it is truncated.
         *                                If places is nonnumeric, BIN2HEX returns the #VALUE! error value.
         *                                If places is negative, BIN2HEX returns the #NUM! error value.
         * @return    string
         */
        public static function BINTOHEX($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                $x = floor($x);
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if (strlen($x) > 10) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (strlen($x) == 10) {
                //    Two's Complement
                return str_repeat('F', 8) . substr(strtoupper(dechex(bindec(substr($x, -9)))), -2);
            }
            $hexVal = (string)strtoupper(dechex(bindec($x)));
            return self::nbrConversionFormat($hexVal, $places);
        }

        /**
         * Formats a number base string value with leading zeroes
         * @param    string  $xVal   The "number" to pad
         * @param    integer $places The length that we want to pad this value
         * @return    string        The padded "number"
         */
        private static function nbrConversionFormat($xVal, $places) {
            if (!is_null($places)) {
                if (strlen($xVal) <= $places) {
                    return substr(str_pad($xVal, $places, '0', STR_PAD_LEFT), -10);
                } else {
                    return PHPExcel_Calculation_Functions::NaN();
                }
            }
            return substr($xVal, -10);
        }

        /**
         * BINTOOCT
         * Return a binary value as octal.
         * Excel Function:
         *        BIN2OCT(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x           The binary number (as a string) that you want to convert. The number
         *                                cannot contain more than 10 characters (10 bits). The most significant
         *                                bit of number is the sign bit. The remaining 9 bits are magnitude bits.
         *                                Negative numbers are represented using two's-complement notation.
         *                                If number is not a valid binary number, or if number contains more than
         *                                10 characters (10 bits), BIN2OCT returns the #NUM! error value.
         * @param    integer $places      The number of characters to use. If places is omitted, BIN2OCT uses the
         *                                minimum number of characters necessary. Places is useful for padding the
         *                                return value with leading 0s (zeros).
         *                                If places is not an integer, it is truncated.
         *                                If places is nonnumeric, BIN2OCT returns the #VALUE! error value.
         *                                If places is negative, BIN2OCT returns the #NUM! error value.
         * @return    string
         */
        public static function BINTOOCT($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_GNUMERIC) {
                $x = floor($x);
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[01]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if (strlen($x) > 10) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (strlen($x) == 10) {
                //    Two's Complement
                return str_repeat('7', 7) . substr(strtoupper(decoct(bindec(substr($x, -9)))), -3);
            }
            $octVal = (string)decoct(bindec($x));
            return self::nbrConversionFormat($octVal, $places);
        }

        /**
         * DECTOBIN
         * Return a decimal value as binary.
         * Excel Function:
         *        DEC2BIN(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x           The decimal integer you want to convert. If number is negative,
         *                                valid place values are ignored and DEC2BIN returns a 10-character
         *                                (10-bit) binary number in which the most significant bit is the sign
         *                                bit. The remaining 9 bits are magnitude bits. Negative numbers are
         *                                represented using two's-complement notation.
         *                                If number < -512 or if number > 511, DEC2BIN returns the #NUM! error
         *                                value.
         *                                If number is nonnumeric, DEC2BIN returns the #VALUE! error value.
         *                                If DEC2BIN requires more than places characters, it returns the #NUM!
         *                                error value.
         * @param    integer $places      The number of characters to use. If places is omitted, DEC2BIN uses
         *                                the minimum number of characters necessary. Places is useful for
         *                                padding the return value with leading 0s (zeros).
         *                                If places is not an integer, it is truncated.
         *                                If places is nonnumeric, DEC2BIN returns the #VALUE! error value.
         *                                If places is zero or negative, DEC2BIN returns the #NUM! error value.
         * @return    string
         */
        public static function DECTOBIN($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)floor($x);
            $r = decbin($x);
            if (strlen($r) == 32) {
                //    Two's Complement
                $r = substr($r, -10);
            } elseif (strlen($r) > 11) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return self::nbrConversionFormat($r, $places);
        }

        /**
         * DECTOHEX
         * Return a decimal value as hex.
         * Excel Function:
         *        DEC2HEX(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x           The decimal integer you want to convert. If number is negative,
         *                                places is ignored and DEC2HEX returns a 10-character (40-bit)
         *                                hexadecimal number in which the most significant bit is the sign
         *                                bit. The remaining 39 bits are magnitude bits. Negative numbers
         *                                are represented using two's-complement notation.
         *                                If number < -549,755,813,888 or if number > 549,755,813,887,
         *                                DEC2HEX returns the #NUM! error value.
         *                                If number is nonnumeric, DEC2HEX returns the #VALUE! error value.
         *                                If DEC2HEX requires more than places characters, it returns the
         *                                #NUM! error value.
         * @param    integer $places      The number of characters to use. If places is omitted, DEC2HEX uses
         *                                the minimum number of characters necessary. Places is useful for
         *                                padding the return value with leading 0s (zeros).
         *                                If places is not an integer, it is truncated.
         *                                If places is nonnumeric, DEC2HEX returns the #VALUE! error value.
         *                                If places is zero or negative, DEC2HEX returns the #NUM! error value.
         * @return    string
         */
        public static function DECTOHEX($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)floor($x);
            $r = strtoupper(dechex($x));
            if (strlen($r) == 8) {
                //    Two's Complement
                $r = 'FF' . $r;
            }
            return self::nbrConversionFormat($r, $places);
        }

        /**
         * DECTOOCT
         * Return an decimal value as octal.
         * Excel Function:
         *        DEC2OCT(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x           The decimal integer you want to convert. If number is negative,
         *                                places is ignored and DEC2OCT returns a 10-character (30-bit)
         *                                octal number in which the most significant bit is the sign bit.
         *                                The remaining 29 bits are magnitude bits. Negative numbers are
         *                                represented using two's-complement notation.
         *                                If number < -536,870,912 or if number > 536,870,911, DEC2OCT
         *                                returns the #NUM! error value.
         *                                If number is nonnumeric, DEC2OCT returns the #VALUE! error value.
         *                                If DEC2OCT requires more than places characters, it returns the
         *                                #NUM! error value.
         * @param    integer $places      The number of characters to use. If places is omitted, DEC2OCT uses
         *                                the minimum number of characters necessary. Places is useful for
         *                                padding the return value with leading 0s (zeros).
         *                                If places is not an integer, it is truncated.
         *                                If places is nonnumeric, DEC2OCT returns the #VALUE! error value.
         *                                If places is zero or negative, DEC2OCT returns the #NUM! error value.
         * @return    string
         */
        public static function DECTOOCT($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                if (PHPExcel_Calculation_Functions::getCompatibilityMode() == PHPExcel_Calculation_Functions::COMPATIBILITY_OPENOFFICE) {
                    $x = (int)$x;
                } else {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[-0123456789.]/', $x, $out)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)floor($x);
            $r = decoct($x);
            if (strlen($r) == 11) {
                //    Two's Complement
                $r = substr($r, -10);
            }
            return self::nbrConversionFormat($r, $places);
        }

        /**
         * HEXTOBIN
         * Return a hex value as binary.
         * Excel Function:
         *        HEX2BIN(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x               the hexadecimal number you want to convert. Number cannot
         *                                    contain more than 10 characters. The most significant bit of
         *                                    number is the sign bit (40th bit from the right). The remaining
         *                                    9 bits are magnitude bits. Negative numbers are represented
         *                                    using two's-complement notation.
         *                                    If number is negative, HEX2BIN ignores places and returns a
         *                                    10-character binary number.
         *                                    If number is negative, it cannot be less than FFFFFFFE00, and
         *                                    if number is positive, it cannot be greater than 1FF.
         *                                    If number is not a valid hexadecimal number, HEX2BIN returns
         *                                    the #NUM! error value.
         *                                    If HEX2BIN requires more than places characters, it returns
         *                                    the #NUM! error value.
         * @param    integer $places          The number of characters to use. If places is omitted,
         *                                    HEX2BIN uses the minimum number of characters necessary. Places
         *                                    is useful for padding the return value with leading 0s (zeros).
         *                                    If places is not an integer, it is truncated.
         *                                    If places is nonnumeric, HEX2BIN returns the #VALUE! error value.
         *                                    If places is negative, HEX2BIN returns the #NUM! error value.
         * @return    string
         */
        public static function HEXTOBIN($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $binVal = decbin(hexdec($x));
            return substr(self::nbrConversionFormat($binVal, $places), -10);
        }

        /**
         * HEXTODEC
         * Return a hex value as decimal.
         * Excel Function:
         *        HEX2DEC(x)
         * @access    public
         * @category  Engineering Functions
         * @param    string $x            The hexadecimal number you want to convert. This number cannot
         *                                contain more than 10 characters (40 bits). The most significant
         *                                bit of number is the sign bit. The remaining 39 bits are magnitude
         *                                bits. Negative numbers are represented using two's-complement
         *                                notation.
         *                                If number is not a valid hexadecimal number, HEX2DEC returns the
         *                                #NUM! error value.
         * @return    string
         */
        public static function HEXTODEC($x) {
            $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return hexdec($x);
        }

        /**
         * HEXTOOCT
         * Return a hex value as octal.
         * Excel Function:
         *        HEX2OCT(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x               The hexadecimal number you want to convert. Number cannot
         *                                    contain more than 10 characters. The most significant bit of
         *                                    number is the sign bit. The remaining 39 bits are magnitude
         *                                    bits. Negative numbers are represented using two's-complement
         *                                    notation.
         *                                    If number is negative, HEX2OCT ignores places and returns a
         *                                    10-character octal number.
         *                                    If number is negative, it cannot be less than FFE0000000, and
         *                                    if number is positive, it cannot be greater than 1FFFFFFF.
         *                                    If number is not a valid hexadecimal number, HEX2OCT returns
         *                                    the #NUM! error value.
         *                                    If HEX2OCT requires more than places characters, it returns
         *                                    the #NUM! error value.
         * @param    integer $places          The number of characters to use. If places is omitted, HEX2OCT
         *                                    uses the minimum number of characters necessary. Places is
         *                                    useful for padding the return value with leading 0s (zeros).
         *                                    If places is not an integer, it is truncated.
         *                                    If places is nonnumeric, HEX2OCT returns the #VALUE! error
         *                                    value.
         *                                    If places is negative, HEX2OCT returns the #NUM! error value.
         * @return    string
         */
        public static function HEXTOOCT($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (strlen($x) > preg_match_all('/[0123456789ABCDEF]/', strtoupper($x), $out)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $octVal = decoct(hexdec($x));
            return self::nbrConversionFormat($octVal, $places);
        }    //    function HEXTOOCT()

        /**
         * OCTTOBIN
         * Return an octal value as binary.
         * Excel Function:
         *        OCT2BIN(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x               The octal number you want to convert. Number may not
         *                                    contain more than 10 characters. The most significant
         *                                    bit of number is the sign bit. The remaining 29 bits
         *                                    are magnitude bits. Negative numbers are represented
         *                                    using two's-complement notation.
         *                                    If number is negative, OCT2BIN ignores places and returns
         *                                    a 10-character binary number.
         *                                    If number is negative, it cannot be less than 7777777000,
         *                                    and if number is positive, it cannot be greater than 777.
         *                                    If number is not a valid octal number, OCT2BIN returns
         *                                    the #NUM! error value.
         *                                    If OCT2BIN requires more than places characters, it
         *                                    returns the #NUM! error value.
         * @param    integer $places          The number of characters to use. If places is omitted,
         *                                    OCT2BIN uses the minimum number of characters necessary.
         *                                    Places is useful for padding the return value with
         *                                    leading 0s (zeros).
         *                                    If places is not an integer, it is truncated.
         *                                    If places is nonnumeric, OCT2BIN returns the #VALUE!
         *                                    error value.
         *                                    If places is negative, OCT2BIN returns the #NUM! error
         *                                    value.
         * @return    string
         */
        public static function OCTTOBIN($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $r = decbin(octdec($x));
            return self::nbrConversionFormat($r, $places);
        }

        /**
         * OCTTODEC
         * Return an octal value as decimal.
         * Excel Function:
         *        OCT2DEC(x)
         * @access    public
         * @category  Engineering Functions
         * @param    string $x            The octal number you want to convert. Number may not contain
         *                                more than 10 octal characters (30 bits). The most significant
         *                                bit of number is the sign bit. The remaining 29 bits are
         *                                magnitude bits. Negative numbers are represented using
         *                                two's-complement notation.
         *                                If number is not a valid octal number, OCT2DEC returns the
         *                                #NUM! error value.
         * @return    string
         */
        public static function OCTTODEC($x) {
            $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            return octdec($x);
        }

        /**
         * OCTTOHEX
         * Return an octal value as hex.
         * Excel Function:
         *        OCT2HEX(x[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    string  $x               The octal number you want to convert. Number may not contain
         *                                    more than 10 octal characters (30 bits). The most significant
         *                                    bit of number is the sign bit. The remaining 29 bits are
         *                                    magnitude bits. Negative numbers are represented using
         *                                    two's-complement notation.
         *                                    If number is negative, OCT2HEX ignores places and returns a
         *                                    10-character hexadecimal number.
         *                                    If number is not a valid octal number, OCT2HEX returns the
         *                                    #NUM! error value.
         *                                    If OCT2HEX requires more than places characters, it returns
         *                                    the #NUM! error value.
         * @param    integer $places          The number of characters to use. If places is omitted, OCT2HEX
         *                                    uses the minimum number of characters necessary. Places is useful
         *                                    for padding the return value with leading 0s (zeros).
         *                                    If places is not an integer, it is truncated.
         *                                    If places is nonnumeric, OCT2HEX returns the #VALUE! error value.
         *                                    If places is negative, OCT2HEX returns the #NUM! error value.
         * @return    string
         */
        public static function OCTTOHEX($x, $places = null) {
            $x      = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            $places = PHPExcel_Calculation_Functions::flattenSingleValue($places);
            if (is_bool($x)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $x = (string)$x;
            if (preg_match_all('/[01234567]/', $x, $out) != strlen($x)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $hexVal = strtoupper(dechex(octdec($x)));
            return self::nbrConversionFormat($hexVal, $places);
        }

        /**
         * IMAGINARY
         * Returns the imaginary coefficient of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMAGINARY(complexNumber)
         * @access    public
         * @category  Engineering Functions
         * @param    string $complexNumber         The complex number for which you want the imaginary
         *                                         coefficient.
         * @return    float
         */
        public static function IMAGINARY($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            return $parsedComplex['imaginary'];
        }

        /**
         * parseComplex
         * Parses a complex number into its real and imaginary parts, and an I or J suffix
         * @param    string $complexNumber The complex number
         * @return    string[]    Indexed on "real", "imaginary" and "suffix"
         */
        public static function parseComplex($complexNumber) {
            $workString = (string)$complexNumber;
            $realNumber = $imaginary = 0;
            //    Extract the suffix, if there is one
            $suffix = substr($workString, -1);
            if (!is_numeric($suffix)) {
                $workString = substr($workString, 0, -1);
            } else {
                $suffix = '';
            }
            //    Split the input into its Real and Imaginary components
            $leadingSign = 0;
            if (strlen($workString) > 0) {
                $leadingSign = (($workString{0} == '+') || ($workString{0} == '-')) ? 1 : 0;
            }
            $power      = '';
            $realNumber = strtok($workString, '+-');
            if (strtoupper(substr($realNumber, -1)) == 'E') {
                $power = strtok('+-');
                ++$leadingSign;
            }
            $realNumber = substr($workString, 0, strlen($realNumber) + strlen($power) + $leadingSign);
            if ($suffix != '') {
                $imaginary = substr($workString, strlen($realNumber));
                if (($imaginary == '') && (($realNumber == '') || ($realNumber == '+') || ($realNumber == '-'))) {
                    $imaginary  = $realNumber . '1';
                    $realNumber = '0';
                } elseif ($imaginary == '') {
                    $imaginary  = $realNumber;
                    $realNumber = '0';
                } elseif (($imaginary == '+') || ($imaginary == '-')) {
                    $imaginary .= '1';
                }
            }
            return [
                'real'      => $realNumber,
                'imaginary' => $imaginary,
                'suffix'    => $suffix
            ];
        }

        /**
         * IMREAL
         * Returns the real coefficient of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMREAL(complexNumber)
         * @access    public
         * @category  Engineering Functions
         * @param    string $complexNumber The complex number for which you want the real coefficient.
         * @return    float
         */
        public static function IMREAL($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            return $parsedComplex['real'];
        }

        /**
         * IMABS
         * Returns the absolute value (modulus) of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMABS(complexNumber)
         * @param    string $complexNumber The complex number for which you want the absolute value.
         * @return    float
         */
        public static function IMABS($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            return sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])
            );
        }

        /**
         * IMCOS
         * Returns the cosine of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMCOS(complexNumber)
         * @param    string $complexNumber The complex number for which you want the cosine.
         * @return    string|float
         */
        public static function IMCOS($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if ($parsedComplex['imaginary'] == 0.0) {
                return cos($parsedComplex['real']);
            } else {
                return self::IMCONJUGATE(self::COMPLEX(cos($parsedComplex['real']) * cosh($parsedComplex['imaginary']), sin($parsedComplex['real']) * sinh($parsedComplex['imaginary']), $parsedComplex['suffix']
                )
                );
            }
        }

        /**
         * IMCONJUGATE
         * Returns the complex conjugate of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMCONJUGATE(complexNumber)
         * @param    string $complexNumber The complex number for which you want the conjugate.
         * @return    string
         */
        public static function IMCONJUGATE($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if ($parsedComplex['imaginary'] == 0.0) {
                return $parsedComplex['real'];
            } else {
                return self::cleanComplex(self::COMPLEX($parsedComplex['real'], 0 - $parsedComplex['imaginary'], $parsedComplex['suffix']
                )
                );
            }
        }

        /**
         * Cleans the leading characters in a complex number string
         * @param    string $complexNumber The complex number to clean
         * @return    string        The "cleaned" complex number
         */
        private static function cleanComplex($complexNumber) {
            if ($complexNumber{0} == '+') {
                $complexNumber = substr($complexNumber, 1);
            }
            if ($complexNumber{0} == '0') {
                $complexNumber = substr($complexNumber, 1);
            }
            if ($complexNumber{0} == '.') {
                $complexNumber = '0' . $complexNumber;
            }
            if ($complexNumber{0} == '+') {
                $complexNumber = substr($complexNumber, 1);
            }
            return $complexNumber;
        }

        /**
         * COMPLEX
         * Converts real and imaginary coefficients into a complex number of the form x + yi or x + yj.
         * Excel Function:
         *        COMPLEX(realNumber,imaginary[,places])
         * @access    public
         * @category  Engineering Functions
         * @param    float  $realNumber           The real coefficient of the complex number.
         * @param    float  $imaginary            The imaginary coefficient of the complex number.
         * @param    string $suffix               The suffix for the imaginary component of the complex number.
         *                                        If omitted, the suffix is assumed to be "i".
         * @return    string
         */
        public static function COMPLEX($realNumber = 0.0, $imaginary = 0.0, $suffix = 'i') {
            $realNumber = (is_null($realNumber)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
            $imaginary  = (is_null($imaginary)) ? 0.0 : PHPExcel_Calculation_Functions::flattenSingleValue($imaginary);
            $suffix     = (is_null($suffix)) ? 'i' : PHPExcel_Calculation_Functions::flattenSingleValue($suffix);
            if (((is_numeric($realNumber)) && (is_numeric($imaginary))) && (($suffix == 'i') || ($suffix == 'j') || ($suffix == ''))) {
                $realNumber = (float)$realNumber;
                $imaginary  = (float)$imaginary;
                if ($suffix == '') {
                    $suffix = 'i';
                }
                if ($realNumber == 0.0) {
                    if ($imaginary == 0.0) {
                        return (string)'0';
                    } elseif ($imaginary == 1.0) {
                        return (string)$suffix;
                    } elseif ($imaginary == -1.0) {
                        return (string)'-' . $suffix;
                    }
                    return (string)$imaginary . $suffix;
                } elseif ($imaginary == 0.0) {
                    return (string)$realNumber;
                } elseif ($imaginary == 1.0) {
                    return (string)$realNumber . '+' . $suffix;
                } elseif ($imaginary == -1.0) {
                    return (string)$realNumber . '-' . $suffix;
                }
                if ($imaginary > 0) {
                    $imaginary = (string)'+' . $imaginary;
                }
                return (string)$realNumber . $imaginary . $suffix;
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         * IMSIN
         * Returns the sine of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMSIN(complexNumber)
         * @param    string $complexNumber The complex number for which you want the sine.
         * @return    string|float
         */
        public static function IMSIN($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if ($parsedComplex['imaginary'] == 0.0) {
                return sin($parsedComplex['real']);
            } else {
                return self::COMPLEX(sin($parsedComplex['real']) * cosh($parsedComplex['imaginary']), cos($parsedComplex['real']) * sinh($parsedComplex['imaginary']), $parsedComplex['suffix']
                );
            }
        }

        /**
         * IMSQRT
         * Returns the square root of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMSQRT(complexNumber)
         * @param    string $complexNumber The complex number for which you want the square root.
         * @return    string
         */
        public static function IMSQRT($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            $theta = self::IMARGUMENT($complexNumber);
            $d1    = cos($theta / 2);
            $d2    = sin($theta / 2);
            $r     = sqrt(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
            if ($parsedComplex['suffix'] == '') {
                return self::COMPLEX($d1 * $r, $d2 * $r);
            } else {
                return self::COMPLEX($d1 * $r, $d2 * $r, $parsedComplex['suffix']);
            }
        }

        /**
         * IMARGUMENT
         * Returns the argument theta of a complex number, i.e. the angle in radians from the real
         * axis to the representation of the number in polar coordinates.
         * Excel Function:
         *        IMARGUMENT(complexNumber)
         * @param    string $complexNumber The complex number for which you want the argument theta.
         * @return    float
         */
        public static function IMARGUMENT($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if ($parsedComplex['real'] == 0.0) {
                if ($parsedComplex['imaginary'] == 0.0) {
                    return 0.0;
                } elseif ($parsedComplex['imaginary'] < 0.0) {
                    return M_PI / -2;
                } else {
                    return M_PI / 2;
                }
            } elseif ($parsedComplex['real'] > 0.0) {
                return atan($parsedComplex['imaginary'] / $parsedComplex['real']);
            } elseif ($parsedComplex['imaginary'] < 0.0) {
                return 0 - (M_PI - atan(abs($parsedComplex['imaginary']) / abs($parsedComplex['real'])));
            } else {
                return M_PI - atan($parsedComplex['imaginary'] / abs($parsedComplex['real']));
            }
        }

        /**
         * IMLOG10
         * Returns the common logarithm (base 10) of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMLOG10(complexNumber)
         * @param    string $complexNumber The complex number for which you want the common logarithm.
         * @return    string
         */
        public static function IMLOG10($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return log10($parsedComplex['real']);
            }
            return self::IMPRODUCT(log10(EULER), self::IMLN($complexNumber));
        }

        /**
         * IMPRODUCT
         * Returns the product of two or more complex numbers in x + yi or x + yj text format.
         * Excel Function:
         *        IMPRODUCT(complexNumber[,complexNumber[,...]])
         * @param    string $complexNumber,... Series of complex numbers to multiply
         * @return    string
         */
        public static function IMPRODUCT() {
            // Return value
            $returnValue  = self::parseComplex('1');
            $activeSuffix = '';
            // Loop through the arguments
            $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
            foreach ($aArgs as $arg) {
                $parsedComplex = self::parseComplex($arg);
                $workValue = $returnValue;
                if (($parsedComplex['suffix'] != '') && ($activeSuffix == '')) {
                    $activeSuffix = $parsedComplex['suffix'];
                } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                    return PHPExcel_Calculation_Functions::NaN();
                }
                $returnValue['real']      = ($workValue['real'] * $parsedComplex['real']) - ($workValue['imaginary'] * $parsedComplex['imaginary']);
                $returnValue['imaginary'] = ($workValue['real'] * $parsedComplex['imaginary']) + ($workValue['imaginary'] * $parsedComplex['real']);
            }
            if ($returnValue['imaginary'] == 0.0) {
                $activeSuffix = '';
            }
            return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix);
        }

        /**
         * IMLN
         * Returns the natural logarithm of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMLN(complexNumber)
         * @param    string $complexNumber The complex number for which you want the natural logarithm.
         * @return    string
         */
        public static function IMLN($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            $logR = log(sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary'])));
            $t    = self::IMARGUMENT($complexNumber);
            if ($parsedComplex['suffix'] == '') {
                return self::COMPLEX($logR, $t);
            } else {
                return self::COMPLEX($logR, $t, $parsedComplex['suffix']);
            }
        }

        /**
         * IMLOG2
         * Returns the base-2 logarithm of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMLOG2(complexNumber)
         * @param    string $complexNumber The complex number for which you want the base-2 logarithm.
         * @return    string
         */
        public static function IMLOG2($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (($parsedComplex['real'] > 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return log($parsedComplex['real'], 2);
            }
            return self::IMPRODUCT(log(EULER, 2), self::IMLN($complexNumber));
        }

        /**
         * IMEXP
         * Returns the exponential of a complex number in x + yi or x + yj text format.
         * Excel Function:
         *        IMEXP(complexNumber)
         * @param    string $complexNumber The complex number for which you want the exponential.
         * @return    string
         */
        public static function IMEXP($complexNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $parsedComplex = self::parseComplex($complexNumber);
            if (($parsedComplex['real'] == 0.0) && ($parsedComplex['imaginary'] == 0.0)) {
                return '1';
            }
            $e  = exp($parsedComplex['real']);
            $eX = $e * cos($parsedComplex['imaginary']);
            $eY = $e * sin($parsedComplex['imaginary']);
            if ($parsedComplex['suffix'] == '') {
                return self::COMPLEX($eX, $eY);
            } else {
                return self::COMPLEX($eX, $eY, $parsedComplex['suffix']);
            }
        }

        /**
         * IMPOWER
         * Returns a complex number in x + yi or x + yj text format raised to a power.
         * Excel Function:
         *        IMPOWER(complexNumber,realNumber)
         * @param    string $complexNumber The complex number you want to raise to a power.
         * @param    float  $realNumber    The power to which you want to raise the complex number.
         * @return    string
         */
        public static function IMPOWER($complexNumber, $realNumber) {
            $complexNumber = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber);
            $realNumber    = PHPExcel_Calculation_Functions::flattenSingleValue($realNumber);
            if (!is_numeric($realNumber)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $parsedComplex = self::parseComplex($complexNumber);
            $r      = sqrt(($parsedComplex['real'] * $parsedComplex['real']) + ($parsedComplex['imaginary'] * $parsedComplex['imaginary']));
            $rPower = pow($r, $realNumber);
            $theta  = self::IMARGUMENT($complexNumber) * $realNumber;
            if ($theta == 0) {
                return 1;
            } elseif ($parsedComplex['imaginary'] == 0.0) {
                return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']);
            } else {
                return self::COMPLEX($rPower * cos($theta), $rPower * sin($theta), $parsedComplex['suffix']);
            }
        }

        /**
         * IMDIV
         * Returns the quotient of two complex numbers in x + yi or x + yj text format.
         * Excel Function:
         *        IMDIV(complexDividend,complexDivisor)
         * @param    string $complexDividend The complex numerator or dividend.
         * @param    string $complexDivisor  The complex denominator or divisor.
         * @return    string
         */
        public static function IMDIV($complexDividend, $complexDivisor) {
            $complexDividend = PHPExcel_Calculation_Functions::flattenSingleValue($complexDividend);
            $complexDivisor  = PHPExcel_Calculation_Functions::flattenSingleValue($complexDivisor);
            $parsedComplexDividend = self::parseComplex($complexDividend);
            $parsedComplexDivisor  = self::parseComplex($complexDivisor);
            if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] != '') && ($parsedComplexDividend['suffix'] != $parsedComplexDivisor['suffix'])) {
                return PHPExcel_Calculation_Functions::NaN();
            }
            if (($parsedComplexDividend['suffix'] != '') && ($parsedComplexDivisor['suffix'] == '')) {
                $parsedComplexDivisor['suffix'] = $parsedComplexDividend['suffix'];
            }
            $d1 = ($parsedComplexDividend['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['imaginary']);
            $d2 = ($parsedComplexDividend['imaginary'] * $parsedComplexDivisor['real']) - ($parsedComplexDividend['real'] * $parsedComplexDivisor['imaginary']);
            $d3 = ($parsedComplexDivisor['real'] * $parsedComplexDivisor['real']) + ($parsedComplexDivisor['imaginary'] * $parsedComplexDivisor['imaginary']);
            $r = $d1 / $d3;
            $i = $d2 / $d3;
            if ($i > 0.0) {
                return self::cleanComplex($r . '+' . $i . $parsedComplexDivisor['suffix']);
            } elseif ($i < 0.0) {
                return self::cleanComplex($r . $i . $parsedComplexDivisor['suffix']);
            } else {
                return $r;
            }
        }

        /**
         * IMSUB
         * Returns the difference of two complex numbers in x + yi or x + yj text format.
         * Excel Function:
         *        IMSUB(complexNumber1,complexNumber2)
         * @param    string $complexNumber1 The complex number from which to subtract complexNumber2.
         * @param    string $complexNumber2 The complex number to subtract from complexNumber1.
         * @return    string
         */
        public static function IMSUB($complexNumber1, $complexNumber2) {
            $complexNumber1 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber1);
            $complexNumber2 = PHPExcel_Calculation_Functions::flattenSingleValue($complexNumber2);
            $parsedComplex1 = self::parseComplex($complexNumber1);
            $parsedComplex2 = self::parseComplex($complexNumber2);
            if ((($parsedComplex1['suffix'] != '') && ($parsedComplex2['suffix'] != '')) && ($parsedComplex1['suffix'] != $parsedComplex2['suffix'])) {
                return PHPExcel_Calculation_Functions::NaN();
            } elseif (($parsedComplex1['suffix'] == '') && ($parsedComplex2['suffix'] != '')) {
                $parsedComplex1['suffix'] = $parsedComplex2['suffix'];
            }
            $d1 = $parsedComplex1['real'] - $parsedComplex2['real'];
            $d2 = $parsedComplex1['imaginary'] - $parsedComplex2['imaginary'];
            return self::COMPLEX($d1, $d2, $parsedComplex1['suffix']);
        }

        /**
         * IMSUM
         * Returns the sum of two or more complex numbers in x + yi or x + yj text format.
         * Excel Function:
         *        IMSUM(complexNumber[,complexNumber[,...]])
         * @param    string $complexNumber,... Series of complex numbers to add
         * @return    string
         */
        public static function IMSUM() {
            // Return value
            $returnValue  = self::parseComplex('0');
            $activeSuffix = '';
            // Loop through the arguments
            $aArgs = PHPExcel_Calculation_Functions::flattenArray(func_get_args());
            foreach ($aArgs as $arg) {
                $parsedComplex = self::parseComplex($arg);
                if ($activeSuffix == '') {
                    $activeSuffix = $parsedComplex['suffix'];
                } elseif (($parsedComplex['suffix'] != '') && ($activeSuffix != $parsedComplex['suffix'])) {
                    return PHPExcel_Calculation_Functions::VALUE();
                }
                $returnValue['real']      += $parsedComplex['real'];
                $returnValue['imaginary'] += $parsedComplex['imaginary'];
            }
            if ($returnValue['imaginary'] == 0.0) {
                $activeSuffix = '';
            }
            return self::COMPLEX($returnValue['real'], $returnValue['imaginary'], $activeSuffix);
        }


        //
        //    Private method to calculate the erf value
        //
        /**
         *    DELTA
         *    Tests whether two values are equal. Returns 1 if number1 = number2; returns 0 otherwise.
         *    Use this function to filter a set of values. For example, by summing several DELTA
         *    functions you calculate the count of equal pairs. This function is also known as the
         *    Kronecker Delta function.
         *    Excel Function:
         *        DELTA(a[,b])
         * @param    float $a The first number.
         * @param    float $b The second number. If omitted, b is assumed to be zero.
         * @return    int
         */
        public static function DELTA($a, $b = 0) {
            $a = PHPExcel_Calculation_Functions::flattenSingleValue($a);
            $b = PHPExcel_Calculation_Functions::flattenSingleValue($b);
            return (int)($a == $b);
        }

        /**
         *    GESTEP
         *    Excel Function:
         *        GESTEP(number[,step])
         *    Returns 1 if number >= step; returns 0 (zero) otherwise
         *    Use this function to filter a set of values. For example, by summing several GESTEP
         *    functions you calculate the count of values that exceed a threshold.
         * @param    float $number            The value to test against step.
         * @param    float $step              The threshold value.
         *                                    If you omit a value for step, GESTEP uses zero.
         * @return    int
         */
        public static function GESTEP($number, $step = 0) {
            $number = PHPExcel_Calculation_Functions::flattenSingleValue($number);
            $step   = PHPExcel_Calculation_Functions::flattenSingleValue($step);
            return (int)($number >= $step);
        }

        /**
         *    ERF
         *    Returns the error function integrated between the lower and upper bound arguments.
         *    Note: In Excel 2007 or earlier, if you input a negative value for the upper or lower bound arguments,
         *            the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
         *            improved, so that it can now calculate the function for both positive and negative ranges.
         *            PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
         *    Excel Function:
         *        ERF(lower[,upper])
         * @param    float $lower         lower bound for integrating ERF
         * @param    float $upper         upper bound for integrating ERF.
         *                                If omitted, ERF integrates between zero and lower_limit
         * @return    float
         */
        public static function ERF($lower, $upper = null) {
            $lower = PHPExcel_Calculation_Functions::flattenSingleValue($lower);
            $upper = PHPExcel_Calculation_Functions::flattenSingleValue($upper);
            if (is_numeric($lower)) {
                if (is_null($upper)) {
                    return self::erfVal($lower);
                }
                if (is_numeric($upper)) {
                    return self::erfVal($upper) - self::erfVal($lower);
                }
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }


        //
        //    Private method to calculate the erfc value
        //
        public static function erfVal($x) {
            if (abs($x) > 2.2) {
                return 1 - self::erfcVal($x);
            }
            $sum  = $term = $x;
            $xsqr = ($x * $x);
            $j    = 1;
            do {
                $term *= $xsqr / $j;
                $sum  -= $term / (2 * $j + 1);
                ++$j;
                $term *= $xsqr / $j;
                $sum  += $term / (2 * $j + 1);
                ++$j;
                if ($sum == 0.0) {
                    break;
                }
            } while (abs($term / $sum) > PRECISION);
            return self::$twoSqrtPi * $sum;
        }

        private static function erfcVal($x) {
            if (abs($x) < 2.2) {
                return 1 - self::erfVal($x);
            }
            if ($x < 0) {
                return 2 - self::ERFC(-$x);
            }
            $a  = $n = 1;
            $b  = $c = $x;
            $d  = ($x * $x) + 0.5;
            $q1 = $q2 = $b / $d;
            $t  = 0;
            do {
                $t  = $a * $n + $b * $x;
                $a  = $b;
                $b  = $t;
                $t  = $c * $n + $d * $x;
                $c  = $d;
                $d  = $t;
                $n  += 0.5;
                $q1 = $q2;
                $q2 = $b / $d;
            } while ((abs($q1 - $q2) / $q2) > PRECISION);
            return self::$oneSqrtPi * exp(-$x * $x) * $q2;
        }

        /**
         *    ERFC
         *    Returns the complementary ERF function integrated between x and infinity
         *    Note: In Excel 2007 or earlier, if you input a negative value for the lower bound argument,
         *        the function would return a #NUM! error. However, in Excel 2010, the function algorithm was
         *        improved, so that it can now calculate the function for both positive and negative x values.
         *            PHPExcel follows Excel 2010 behaviour, and accepts nagative arguments.
         *    Excel Function:
         *        ERFC(x)
         * @param    float $x The lower bound for integrating ERFC
         * @return    float
         */
        public static function ERFC($x) {
            $x = PHPExcel_Calculation_Functions::flattenSingleValue($x);
            if (is_numeric($x)) {
                return self::erfcVal($x);
            }
            return PHPExcel_Calculation_Functions::VALUE();
        }

        /**
         *    getConversionGroups
         *    Returns a list of the different conversion groups for UOM conversions
         * @return    array
         */
        public static function getConversionGroups() {
            $conversionGroups = [];
            foreach (self::$conversionUnits as $conversionUnit) {
                $conversionGroups[] = $conversionUnit['Group'];
            }
            return array_merge(array_unique($conversionGroups));
        }

        /**
         *    getConversionGroupUnits
         *    Returns an array of units of measure, for a specified conversion group, or for all groups
         * @param    string $group The group whose units of measure you want to retrieve
         * @return    array
         */
        public static function getConversionGroupUnits($group = null) {
            $conversionGroups = [];
            foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
                if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                    $conversionGroups[$conversionGroup['Group']][] = $conversionUnit;
                }
            }
            return $conversionGroups;
        }

        /**
         *    getConversionGroupUnitDetails
         * @param    string $group The group whose units of measure you want to retrieve
         * @return    array
         */
        public static function getConversionGroupUnitDetails($group = null) {
            $conversionGroups = [];
            foreach (self::$conversionUnits as $conversionUnit => $conversionGroup) {
                if ((is_null($group)) || ($conversionGroup['Group'] == $group)) {
                    $conversionGroups[$conversionGroup['Group']][] = [
                        'unit'        => $conversionUnit,
                        'description' => $conversionGroup['Unit Name']
                    ];
                }
            }
            return $conversionGroups;
        }

        /**
         *    getConversionMultipliers
         *    Returns an array of the Multiplier prefixes that can be used with Units of Measure in CONVERTUOM()
         * @return    array of mixed
         */
        public static function getConversionMultipliers() {
            return self::$conversionMultipliers;
        }

        /**
         *    CONVERTUOM
         *    Converts a number from one measurement system to another.
         *    For example, CONVERT can translate a table of distances in miles to a table of distances
         *    in kilometers.
         *    Excel Function:
         *        CONVERT(value,fromUOM,toUOM)
         * @param    float  $value   The value in fromUOM to convert.
         * @param    string $fromUOM The units for value.
         * @param    string $toUOM   The units for the result.
         * @return    float
         */
        public static function CONVERTUOM($value, $fromUOM, $toUOM) {
            $value   = PHPExcel_Calculation_Functions::flattenSingleValue($value);
            $fromUOM = PHPExcel_Calculation_Functions::flattenSingleValue($fromUOM);
            $toUOM   = PHPExcel_Calculation_Functions::flattenSingleValue($toUOM);
            if (!is_numeric($value)) {
                return PHPExcel_Calculation_Functions::VALUE();
            }
            $fromMultiplier = 1.0;
            if (isset(self::$conversionUnits[$fromUOM])) {
                $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
            } else {
                $fromMultiplier = substr($fromUOM, 0, 1);
                $fromUOM        = substr($fromUOM, 1);
                if (isset(self::$conversionMultipliers[$fromMultiplier])) {
                    $fromMultiplier = self::$conversionMultipliers[$fromMultiplier]['multiplier'];
                } else {
                    return PHPExcel_Calculation_Functions::NA();
                }
                if ((isset(self::$conversionUnits[$fromUOM])) && (self::$conversionUnits[$fromUOM]['AllowPrefix'])) {
                    $unitGroup1 = self::$conversionUnits[$fromUOM]['Group'];
                } else {
                    return PHPExcel_Calculation_Functions::NA();
                }
            }
            $value *= $fromMultiplier;
            $toMultiplier = 1.0;
            if (isset(self::$conversionUnits[$toUOM])) {
                $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
            } else {
                $toMultiplier = substr($toUOM, 0, 1);
                $toUOM        = substr($toUOM, 1);
                if (isset(self::$conversionMultipliers[$toMultiplier])) {
                    $toMultiplier = self::$conversionMultipliers[$toMultiplier]['multiplier'];
                } else {
                    return PHPExcel_Calculation_Functions::NA();
                }
                if ((isset(self::$conversionUnits[$toUOM])) && (self::$conversionUnits[$toUOM]['AllowPrefix'])) {
                    $unitGroup2 = self::$conversionUnits[$toUOM]['Group'];
                } else {
                    return PHPExcel_Calculation_Functions::NA();
                }
            }
            if ($unitGroup1 != $unitGroup2) {
                return PHPExcel_Calculation_Functions::NA();
            }
            if (($fromUOM == $toUOM) && ($fromMultiplier == $toMultiplier)) {
                //    We've already factored $fromMultiplier into the value, so we need
                //        to reverse it again
                return $value / $fromMultiplier;
            } elseif ($unitGroup1 == 'Temperature') {
                if (($fromUOM == 'F') || ($fromUOM == 'fah')) {
                    if (($toUOM == 'F') || ($toUOM == 'fah')) {
                        return $value;
                    } else {
                        $value = (($value - 32) / 1.8);
                        if (($toUOM == 'K') || ($toUOM == 'kel')) {
                            $value += 273.15;
                        }
                        return $value;
                    }
                } elseif ((($fromUOM == 'K') || ($fromUOM == 'kel')) && (($toUOM == 'K') || ($toUOM == 'kel'))) {
                    return $value;
                } elseif ((($fromUOM == 'C') || ($fromUOM == 'cel')) && (($toUOM == 'C') || ($toUOM == 'cel'))) {
                    return $value;
                }
                if (($toUOM == 'F') || ($toUOM == 'fah')) {
                    if (($fromUOM == 'K') || ($fromUOM == 'kel')) {
                        $value -= 273.15;
                    }
                    return ($value * 1.8) + 32;
                }
                if (($toUOM == 'C') || ($toUOM == 'cel')) {
                    return $value - 273.15;
                }
                return $value + 273.15;
            }
            return ($value * self::$unitConversions[$unitGroup1][$fromUOM][$toUOM]) / $toMultiplier;
        }
    }
